The following text comes from the AcresUSA Soil Health Primer Resources page. A direct link to the PDF can be viewed here.
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This article focuses on the principle of "Livestock Integration"

Livestock give to the soil something neither man nor machine can synthesize or impersonate. The relationship between animals and land is mutually beneficial, each relying on the other to sustain, to thrive, and to profit. Integrating livestock into a farm or starting a ranch to raise livestock is a commitment, a responsibility, and one of the most efficient ways to enhance soil health. Animals can play several roles as soil health improvement tool.

According to the United States Department of Agriculture (USDA), livestock can provide the following benefits to the soil:

• They can convert high-carbon annual crop residue to low-carbon organic material via fall and/or winter grazing. This action will balance carbon/ nitrogen ratios and manage crop rotation residue for no-till producers.
• They can promote perennial pasture regrowth through spring and summer grazing. Short exposure periods followed by long recovery periods allow plants to keep growing and to harvest additional sunlight and CO2.
• They can reduce nutrient export from the soil. When livestock graze in the field, nutrients, minerals, vitamins, and carbon are recycled.
• They can manage weed pressure without herbicides.
• They can graze cover crops and/or crop residues, allowing perennial pastures to rest, while providing the livestock a higher-nutrient diet.
• If put on pasture instead of being in confinement, they can reduce waste and can help manage water quality and nutrient management concerns.

The benefits of using livestock are plentiful, and there are many ways to integrate them into soil- health-driven farming systems.

USDA recommends starting with grazing cover crops on annual crop residues in the winter and fall. The next step could be summer grazing on a full- season cover crop, following up on the same field during the fall or winter. Cattle can also eat bale feed on fields for added nutrient inputs. Yet another option is to seed perennial pastures to use as part of a crop rotation. These actions will stimulate the life in the soil and can be an alternative to confined feeding.

While integrating livestock into an existing operation is perhaps the most challenging of the principles of soil health to implement, it has the potential to bring the greatest benefits.

“When integrating any livestock of any kind, start small,” said Mollie Wells, owner of the Rio Grande Dairy in San Luis. “People do get very excited and sometimes bring in a whole bunch of animals. Then there is disease. Then there is overgrazing. Once you have a system in place, then bring in animal diversity. There are soil health and economic benefits once you are educated.”